# Selecting Reference Orbit for Fractal Rendering with Perturbation Theory

I have been trying to implement the perturbation algorithm for rendering fractals, as per this article: http://www.superfractalthing.co.nf/sft_maths.pdf

Let's say we simply focus on the first of the method, part up to equation 1, neglecting the series approximation part at the end to speed up calculations.

My question is regarding the reference orbit. Since you record the orbit of a reference point, and calculate the other points based on that reference, doesn't that imply that the reference need to have an iteration count (before its norm reaches 2) larger than all the other calculated points/pixels in the image? For example, how would you go about calculating the points in the image needing 10000 iterations before diverging when your reference diverges after 1000? If you indeed need the reference to diverge last, how would you choose such a point?

Thanks.